As presented, perhaps not much, but it can be helpful when you have players with varying amounts of data. If we know there are correlations among the players, then we can get better inferences for players that have fewer games.
You never want to extrapolate beyond the lengthscale of the GP, that’s true. If you were interested in extrapolation, you would either have another function to use as the GP’s mean function, or have an additive kernel that includes a component with a longer lengthscale.